// -----------------------------
// projects/c++/collatz/main.c++
// Copyright (C) 2009
// Glenn P. Downing
// -----------------------------

/*
To run the tests:
    % g++ -ansi -pedantic -lcppunit -ldl -Wall -DTEST main.c++ -o main.app
    % valgrind main.app

To run the program:
    % g++ -ansi -pedantic -Wall main.c++ -o main.app
    % valgrind main.app < Primes.in > Primes.out

To configure Doxygen:
    doxygen -g
That creates the file Doxyfile.
Make the following edits:
    EXTRACT_ALL            = YES
    EXTRACT_PRIVATE        = YES
    EXTRACT_STATIC         = YES
    GENERATE_LATEX         = NO

To document the program:
    doxygen Doxyfile
*/

// --------
// includes
// --------

#include <cassert>  // assert
#include <iostream> // cin, cout, endl, ios_base, istream, ostream

#ifdef TEST
    #include "cppunit/TestSuite.h"      // TestSuite
    #include "cppunit/TextTestRunner.h" // TestRunner
#endif // TEST

// -------
// defines
// -------

#ifdef ONLINE_JUDGE
    #define NDEBUG
#endif

// -------
// globals
// -------

int v; // input: don't change after reading
int i,j,k,l; // output
bool valid;
int primes[445]={2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71,
73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173,
179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281,
283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409,
419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541,
547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659,
661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809,
811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941,
947, 953, 967, 971, 977, 983, 991, 997, 1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069,
1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223,
1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291, 1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373,
1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, 1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511,
1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, 1597, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657,
1663, 1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733, 1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811,
1823, 1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 1889, 1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987,
1993, 1997, 1999, 2003, 2011, 2017, 2027, 2029, 2039, 2053, 2063, 2069, 2081, 2083, 2087, 2089, 2099, 2111, 2113, 2129,
2131, 2137, 2141, 2143, 2153, 2161, 2179, 2203, 2207, 2213, 2221, 2237, 2239, 2243, 2251, 2267, 2269, 2273, 2281, 2287,
2293, 2297, 2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357, 2371, 2377, 2381, 2383, 2389, 2393, 2399, 2411, 2417, 2423,
2437, 2441, 2447, 2459, 2467, 2473, 2477, 2503, 2521, 2531, 2539, 2543, 2549, 2551, 2557, 2579, 2591, 2593, 2609, 2617,
2621, 2633, 2647, 2657, 2659, 2663, 2671, 2677, 2683, 2687, 2689, 2693, 2699, 2707, 2711, 2713, 2719, 2729, 2731, 2741,
2749, 2753, 2767, 2777, 2789, 2791, 2797, 2801, 2803, 2819, 2833, 2837, 2843, 2851, 2857, 2861, 2879, 2887, 2897, 2903,
2909, 2917, 2927, 2939, 2953, 2957, 2963, 2969, 2971, 2999, 3001, 3011, 3019, 3023, 3037, 3041, 3049, 3061, 3067, 3079,
3083, 3089, 3109, 3119, 3121};


// ----
// read
// ----

/**
 * reads an int into v
 * @return true if that succeeds, false otherwise
 */
bool read (std::istream& in) {
    	if (!(in >> v))
        	return false;
    	return true;}

// -------
// isPrime
// -------

/**
 * checks to see if number n is prime
 * @return true if prime, false if not
 */
bool isPrime(int n){
	for( int x =0 ; x< 445; ++x){		// iterate through cache
		if( n == primes[x])		// if n is in cache, # is prime
			return true;
		if(n % primes[x] == 0)		// else if cur # in cache divides n, # is NOT prime
			return false;
	}
	return true;
}


// ----
// eval
// ----

/**
 * computes four primes that add up to v
 * and stores the result in v
 */
void eval () {
	valid = v>=8 && v<=10000000;
	if(valid){
		assert (v>=8 && v<=10000000);

		k=(v%2 ==0)? 2 : 3;
		l=2;			// first 2 primes can always be 2,2 or 2,3 based on v (odd or even)
		int mid = (v-k-l)>>1;	// middle number of resulting total after v-k-l
		int x = 0;
		bool done = isPrime(mid);
		while(!done){
			if((mid+x)%2 == 1)
				++x;
			++x;
			done = isPrime(mid+x) && isPrime(mid-x);	// if mid+x and mid-x are both prime, done
		}							// because mid+x + mid - x = 2*mid = v-k-l
		i = mid + x;
		j = mid - x;						// set i,j

		assert( (i+j+k+l) == v );
	}
}

// -----
// print
// -----

/**
 * prints the values of i, j, k, and l if valid
 * otherwise, prints "Impossible."
 */
void print (std::ostream& out) {
	if (valid)
    		out << i << " " << j << " " << k << " " << l << std::endl;
	else
		out << "Impossible."<< std::endl;
}

// -----
// tests
// -----

#ifdef TEST
    #include "TestPrimes.h"
#endif // TEST

// ----
// main
// ----

/**
 * either runs the tests or runs the program
 */
int main () {
    	using namespace std;
    	ios_base::sync_with_stdio(false); // turn off synchronization with C I/O

    	#ifdef TEST
        // ----------
        // unit tests
        // ----------

        	CppUnit::TextTestRunner tr;
        	tr.addTest(TestPrimes::suite());
        	tr.run();
    	#else
        // -------
        // program
        // -------

        while (read(cin)) {
            eval();
            print(cout);}
    	#endif // TEST

    	return 0;} 
